What is... game theory

What is...

Mind + Money

Game theory is about decision making but not, as the term may suggest, by throwing dice or picking a random card. Game theory relates to situations when decisions depend on the actions of others. The approach has been used in a variety of fields including environmental, social, political and business. It is also useful for understanding the way individuals and families choose to spend and save.

The more glamorous acknowledgement of game theorists include the portrayal of economist John Nash in film A Beautiful Mind and the awarding of the 2012 Nobel Prize in Economics for research in the field.

Playing the game
Although called game theory, it does not involve the type of games that typically spring to mind. Here, a ‘game’ is a mathematical representation of a real-world situation. A person (or ‘player’) in the situation tries to pick a strategy to get the best result for themself.
But when planning this strategy, the player must consider what other players will do. Because of this, beliefs about moves the player’s opponent will likely make influence the player’s choices. Further, the player must also consider how opponents may adjust their strategies based on what they think the first player will do.

The Prisoner’s Dilemma
The “Prisoner’s Dilemma” is a well-known game theory illustration. In it, two thieves (called Albert and Barbara) burgle a jewellery store and are brought in to the police station and placed in separate cells for questioning. The police have some evidence to charge the pair with previous petty crime but need a confession to charge them for the jewellery store heist.
The jail sentences handed down to each will depend on the outcome of the questioning. If neither Albert nor Barbara confesses to the heist, they will each get one year in jail for their previous minor misdeeds. If both confess, they will each be given five years in jail for the major jewellery theft. If one confesses that the pair committed the crime, but the other doesn’t, the confessor will be granted amnesty but the other will face eight years in jail: five for the crime plus three extra for obstructing justice.
What happens?
Albert considers what Barbara will do: if she keeps quiet, he can confess and avoid prison. But if she confesses, he should confess too, to avoid getting stuck with eight years in jail. Barbara goes through the same thought process.
So they each confess and are locked up for five years. But both could have been much better off (if we leave truth and ethics to one side) if they had committed to keep quiet and received a sentence of just one year each.
The prisoner’s dilemma shows that each person following their dominant strategy, in this case confessing, doesn’t always lead to the best outcome.

Playing at home
Game theory is not confined to prisons or economics classrooms. In the home, decisions about the division of housework, choice of entertainment and how to spend and invest can all be thought of as “games”. Family members are players and managing the household budget is the game. Many household decisions require cooperation and communication. With this comes the possibility for negotiation, bargaining and – at times – threats.

What’s mine is…
Couples often vow to share what is theirs. What’s perhaps surprising then is that research suggests having a higher share of pre-marital assets may mean more bargaining power for years to come. A separate study abstract shows that the type of spending mattered. If the increase to the household pool of funds came from a man, the study found increased spending on transport. Whereas an increase to female income was associated with increased spending on children’s clothing.

Origins of game theory
Developed by mathematician John von Neumann and economist Oskar Morgenstern, game theory was introduced to the wider public in their 1944 book Theory of Games and Economic Behavior. Shortly after, economist John Nash built on the theory extensively. Nash’s contribution to the field was so great that his name is firmly embedded in its language; for example, a Nash Equilibrium describes a set of strategies where no one would be better off by changing his or her position. Nash’s life was portrayed in the 2001 Oscar-winning movie A Beautiful Mind.
Many game theoretic models assume that everyone is rational and infinitely intelligent but newer contributions to the field (such as behavioural economist Colin Camerer’s Behavioral Game Theory) recognise that while this assumption makes it easier to model interactions mathematically, real life often does not fit this ideal.

A Nobel achievement
There have been many notable advancements in game theory over the years, and research in the field continues today. In October 2012, Al Roth and Lloyd Shapley were awarded the Nobel Prize in Economics for their matching algorithm work in game theory. The Economist write up is here.

Game theory has been used in areas as diverse as business, evolutionary biology, voting, auctions, and environmental degradation. Understanding its fundamentals can be very rewarding and may even change the way you make everyday decisions.

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